iPad 1 no longer connecting through dock - can anyone help?

All of a sudden, my iPad 1 dock connector stopped working a few weeks ago: would no longer sync on iTunes, would not react to the insertion of the camera connection kit, would no longer work with the HDMI connector and would no longer charge properly.

If I switch off the iPad and connect it to the Mac or the wall charger, the iPad does detect the connection and automatically start up. But iTunes never detects the iPad and the iPad never enters proper charging

If I leave it long enough connected to the wall charger, it does charge, but just much slower (and it nevers shows the "charging" icon). Once charged, its battery life is as good as ever so it does not seem to be a battery issue.

I did try all the restore options, without any change. I also bought a replacement iPad connector flexible cable (internal part), performed the replacement, but without any change!

Since the iPad is out of warranty, paying 400€ to Apple for a refurbished iPad 3G 64Go is the only official "repair" option, and that does not seem too smart...

Anything else I can try before giving up? I read several threads on similar dock connector issues on the iPad 1 and some mentioned loosening some screws holding the internal iPad connector flexible cable solved the issue Which one would it be?

As long as I can charge it at night, I can keep using it on WiFi and 3G, but no longer being able to use the camera connection kit or the display cable is a pain

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